Connect 2 different wire gauge; is the smaller gauge affecting the capacity of the bigger wire gauge?

Your question is an interesting one can be solved by a little bit of thought - but the short answer is that each gauge and type of wire has its own maximum current capacity (ampacity) and connecting the two together does not change the fact that the 16AWG portion has its own maximum current rating and the 22AWG portion has its own maximum current rating. Both maximum current ratings must be respected.

The long answer:

There's actually two different issues which are being mixed together. The first that you have mentioned is maximum current carrying capacity (or ampacity) and this refers to the maximum current the cable is rated to carry so it doesn't cause damage to its insulation. This is not necessarily a good current level to operate at, because the second issue is cable resistance which causes a voltage drop. Lets say your long run is 20m with 16AWG wire with an 80 degrees C rated insulation. Its maximum current capacity is 19A. But if you tried to pass 19A through the cable, you would lose 10.01V (190W of heat) with only 1.99V remaining to power your device. So in most practical instances, your cable choice should be constrained by resistive losses rather than the cable current carrying capacity. However, you can size your cable protection to respect the maximum ampacity to avoid cable damage during fault conditions (i.e. use a 15A fuse for example).

Knowing this, the ampacity of your 16AWG cable may be 19A and the ampacity of your 22AWG cable might be 8A. How does this affect things? Well to put it simply, the ampacity of each size of cable must be respected. Think of a home electrical distribution supply - the main supply from your utility comes through thick cables and may be fused at 100A (cable has an ampacity at least 100A). But this is then connected to your end circuits including power points and appliances through thinner wire - mostly with ampacity around 20-30A. This is why each circuit has its own fuse or circuit breaker protecting that branch from fault current induced damage. This is an instance where one thick cable is powering many appliances through a number of thinner wires.

But it also means that say you run one 16AWG run from the battery to a central point (with a fuse rated appropriately), you can also run several 22AWG runs from this point outward (separately fused for the 22AWG wire) depending on the total load as long as the total current on the 16AWG section doesn't exceed its limit, the total current on each 22AWG section doesn't exceed its limit and you have sufficient voltage remaining to power your end device. In practice, if you are just powering one device, or you won't exceed the ampacity of the thinnest wire in the system, you could use a single fuse to protect the whole set - i.e. you use a 5A fuse with the whole system when 16AWG can handle up to 19A and 22AWG can handle up to 8A, this is always going to be safe, but on the downside, it means you might not be able to make the best use of the wire in case you might want to add loads later.

Regardless, I doubt that the ampacity will cause a problem - it's more likely that the resistance in your wires will make it hard to high currents for run long distances especially at low voltages. Even to push 5A through a distance of 20m will require 9AWG or thicker according to this Voltage Drop Calculator, so to avoid losses, it's best to use as thick of a cable as possible to run the maximum distance. Otherwise, in specialist scenarios, it is possible to increase voltage and then decrease it again later, to reduce transmission losses but the conversion will itself introduce losses.

- Gough

Your question is an interesting one can be solved by a little bit of thought - but the short answer is that each gauge and type of wire has its own maximum current capacity (ampacity) and connecting the two together does not change the fact that the 16AWG portion has its own maximum current rating and the 22AWG portion has its own maximum current rating. Both maximum current ratings must be respected.

The long answer:

There's actually two different issues which are being mixed together. The first that you have mentioned is maximum current carrying capacity (or ampacity) and this refers to the maximum current the cable is rated to carry so it doesn't cause damage to its insulation. This is not necessarily a good current level to operate at, because the second issue is cable resistance which causes a voltage drop. Lets say your long run is 20m with 16AWG wire with an 80 degrees C rated insulation. Its maximum current capacity is 19A. But if you tried to pass 19A through the cable, you would lose 10.01V (190W of heat) with only 1.99V remaining to power your device. So in most practical instances, your cable choice should be constrained by resistive losses rather than the cable current carrying capacity. However, you can size your cable protection to respect the maximum ampacity to avoid cable damage during fault conditions (i.e. use a 15A fuse for example).

Knowing this, the ampacity of your 16AWG cable may be 19A and the ampacity of your 22AWG cable might be 8A. How does this affect things? Well to put it simply, the ampacity of each size of cable must be respected. Think of a home electrical distribution supply - the main supply from your utility comes through thick cables and may be fused at 100A (cable has an ampacity at least 100A). But this is then connected to your end circuits including power points and appliances through thinner wire - mostly with ampacity around 20-30A. This is why each circuit has its own fuse or circuit breaker protecting that branch from fault current induced damage. This is an instance where one thick cable is powering many appliances through a number of thinner wires.

But it also means that say you run one 16AWG run from the battery to a central point (with a fuse rated appropriately), you can also run several 22AWG runs from this point outward (separately fused for the 22AWG wire) depending on the total load as long as the total current on the 16AWG section doesn't exceed its limit, the total current on each 22AWG section doesn't exceed its limit and you have sufficient voltage remaining to power your end device. In practice, if you are just powering one device, or you won't exceed the ampacity of the thinnest wire in the system, you could use a single fuse to protect the whole set - i.e. you use a 5A fuse with the whole system when 16AWG can handle up to 19A and 22AWG can handle up to 8A, this is always going to be safe, but on the downside, it means you might not be able to make the best use of the wire in case you might want to add loads later.

Regardless, I doubt that the ampacity will cause a problem - it's more likely that the resistance in your wires will make it hard to high currents for run long distances especially at low voltages. Even to push 5A through a distance of 20m will require 9AWG or thicker according to this Voltage Drop Calculator, so to avoid losses, it's best to use as thick of a cable as possible to run the maximum distance. Otherwise, in specialist scenarios, it is possible to increase voltage and then decrease it again later, to reduce transmission losses but the conversion will itself introduce losses.

- Gough